She uses them as she calls on families across the country, as part of the second phase of a study she is leading through her work as an assistant professor with the Rudd Adoption Research Program at the University of Massachusetts Amherst.

Once she’s arrived at a home, Farr breaks the ice by spreading a blanket on the floor, unveiling her backpack of toys from shape sorters to tea sets and action figures and letting the family play together while she disappears into the background. A video camera captures the dynamics.

The work began in 2007 with co-collaborator Charlotte J. Patterson of the University of Virginia. And after two years of collecting data — through these personal visits and surveys the parents and the family’s day care providers completed — the pair have released their initial findings in the July/August issue of “Child Development,” positing that parents’ sexual orientation is not linked to behavioral problems in children.

“We’re not seeing major differences in children, parents, couples or families on the basis of parents’ sexual orientation,” Farr said. “What we do find is that the family processes seem to matter more than family structure — whether the parents are stressed about their parenting matters more than if a family has two moms or two dads.” Farr said the pair hopes their work has positive ramifications across the country, removing barriers to adoption by same-sex couples and serving to advocate for more supportive laws and programs for same-sex families.

“What we think is particularly important about our research is it suggests that lesbian and gay adults should be equally considered to be adoptive parents. It’s clear from our results that children in our families are thriving and that these are happy and healthy families,” Farr said.

For the study, Farr and Patterson recruited families through five adoption agencies across the United States; 104 families participated, 25 headed by lesbian partners, 29 by gay male partners and 50 by heterosexual couples. The adoptive children, between 1 and 5 years old, with the majority around 3 years old, had been placed with them at birth or within the first few weeks of life; some had siblings.

“We were interested in a number of areas of family life,” Farr said. “We were interested in how children were doing, how the parents talked about their parenting practices and in their couple relationship. We were also interested in overall family functioning.”

Farr began her work unofficially while studying for a master’s and doctoral degree in developmental psychology at the University of Virginia. Patterson, an expert in lesbian and gay parenting, was her advisor.

The two paired up on the study, funded by the Williams Institute at UCLA and the Lesbian Health Fund, to shed further light on the subject of same-sex parenting.

“There’s very little research overall on these topics,” Farr said. “It seemed like a really important topic in terms of gathering empirical research to address these public debates.”

Farr said she recently began the second phase of the study, following up with families; children who are the focus are now 7 or 8. “It will be a little bit of time before we are able to publish our results in (this phase),” she added.

Other findings from the first phase of the study:

■ Parents who reported feeling unsatisfied in their relationship with their partner also reported behavioral problems in their child, or children, Farr added.

■ Same-sex couples are more likely to split chores evenly.

■ Heterosexual couples are more likely to “specialize” in tasks, with mothers generally doing more than fathers.

“We’re not saying these families are identical, but when there are these differences in family life, they’re not linked with qualitative differences in how children are doing,” Farr said.